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An improved certificateless strong keyinsulated signature scheme in the standard model
Some new results on cross correlation of $p$ary $m$sequence and its decimated sequence
1.  School of Mathemetics & Computation Science, Anqing Normal University, Anqing, Anhui 246133, China 
2.  Department of Mathematic and Statistics, Centtal China Normal University, Wuhan, Hubei 430079, China 
3.  Department of Mathematic Sciences, Yangzhou University, Yangzhou, Jiangsu 225002, China, China 
References:
[1] 
A. W. Bluher, On $x^{q+1}+ax+b$, Finite Fields Appl., 10 (2004), 285305. doi: 10.1016/j.ffa.2003.08.004. 
[2] 
W. Chen, J. Luo and Y. Tang, Exponential sums from half quadratic forms and its applications, in Proc. ISIT'14, 2014, 31453149. 
[3] 
S. T. Choi, J. S. No and H. Chung, On the crosscorrelation of a ternary msequence of period $3^{4k+2}1$ and its decimated sequence by $(3^{2k+1}+1)^{2}$ over 8, in Proc. ISIT'10, 2010, 12681271. 
[4] 
S. T. Choi, J. S. No and H. Chung, On the crosscorrelation of a $p$ary msequence of period $p^{2m}1$ and its decimated sequence by $\frac{(p^m+1)^2}{2(p+1)}$, IEEE Trans. Inf. Theory, 58 (2012), 18731879. doi: 10.1109/TIT.2011.2177573. 
[5] 
H. Dobbertin, P. Felke and T. Helleseth, Niho type cross correlation functions via Dickson polynomials and Kloosterman sums, IEEE Trans. Inf. Theory, 52 (2006), 613627. doi: 10.1109/TIT.2005.862094. 
[6] 
T. Helleseth, Some results about the crosscorrelation function between two maximallinear sequence, Discrete Math., 16 (1976), 209232. 
[7] 
R. Lidl and H. Niederreiter, Finite Fields, AddisonWesley, Boston, 1983. 
[8] 
J. Luo and K. Feng, On the weight distribution of two classes of cyclic codes, IEEE Trans. Inf. Theory, 54 (2008), 53325344. doi: 10.1109/TIT.2008.2006424. 
[9] 
J. Luo and K. Feng, Cyclic codes and sequences from generalized CoulterMatthews function, IEEE Trans. Inf. Theory, 54 (2008), 53455353. doi: 10.1109/TIT.2008.2006394. 
[10] 
J. Luo, T. Helleseth and A. Kholosha, Two nonbinary sequences with sixvalued cross correlation, in Proc. IWSDA'11, 2011, 4447. 
[11] 
J, Luo, Y. Tang and H. Wang, Exponential sums, cyclic codes and sequences: the odd characteristic Kasami case,, preprint, (). 
[12] 
G. J. Ness, T. Helleseth and A. Kholosha, On the correlation distribution of the CoulterMatthews decimation, IEEE Trans. Inf. Theory, 52 (2006), 22412247. doi: 10.1109/TIT.2006.872857. 
[13] 
E. Y. Seo, Y. S. Kim, J. S. No and D. J. Shin, Crosscorrelation distribution of pary msequence of period $p^{4k}1$ and its decimated sequences by $(\frac{p^{2k}+1}{2})^{2}$, IEEE Trans. Inf. Theory, 54 (2008),31403149. doi: 10.1109/TIT.2008.924694. 
[14] 
Y. Sun, Z. Wang, H. Li and T. Yan, The crosscorrelation distribution of a $p$ary msequence of period $p^{2k}1$ and its decimated sequence by $\frac{(p^k+1)^2}{2(p^e+1)}$, Adv. Math. Commun., 7 (2013), 409424. doi: 10.3934/amc.2013.7.409. 
[15] 
Y. Xia, C. Li, X. Zeng and T. Helleseth, Some results on crosscorrelation distribution between a $p$ary $m$sequence and its decimated sequences, IEEE Trans. Inf. Theory, 60 (2014), 73687381. doi: 10.1109/TIT.2014.2350775. 
show all references
References:
[1] 
A. W. Bluher, On $x^{q+1}+ax+b$, Finite Fields Appl., 10 (2004), 285305. doi: 10.1016/j.ffa.2003.08.004. 
[2] 
W. Chen, J. Luo and Y. Tang, Exponential sums from half quadratic forms and its applications, in Proc. ISIT'14, 2014, 31453149. 
[3] 
S. T. Choi, J. S. No and H. Chung, On the crosscorrelation of a ternary msequence of period $3^{4k+2}1$ and its decimated sequence by $(3^{2k+1}+1)^{2}$ over 8, in Proc. ISIT'10, 2010, 12681271. 
[4] 
S. T. Choi, J. S. No and H. Chung, On the crosscorrelation of a $p$ary msequence of period $p^{2m}1$ and its decimated sequence by $\frac{(p^m+1)^2}{2(p+1)}$, IEEE Trans. Inf. Theory, 58 (2012), 18731879. doi: 10.1109/TIT.2011.2177573. 
[5] 
H. Dobbertin, P. Felke and T. Helleseth, Niho type cross correlation functions via Dickson polynomials and Kloosterman sums, IEEE Trans. Inf. Theory, 52 (2006), 613627. doi: 10.1109/TIT.2005.862094. 
[6] 
T. Helleseth, Some results about the crosscorrelation function between two maximallinear sequence, Discrete Math., 16 (1976), 209232. 
[7] 
R. Lidl and H. Niederreiter, Finite Fields, AddisonWesley, Boston, 1983. 
[8] 
J. Luo and K. Feng, On the weight distribution of two classes of cyclic codes, IEEE Trans. Inf. Theory, 54 (2008), 53325344. doi: 10.1109/TIT.2008.2006424. 
[9] 
J. Luo and K. Feng, Cyclic codes and sequences from generalized CoulterMatthews function, IEEE Trans. Inf. Theory, 54 (2008), 53455353. doi: 10.1109/TIT.2008.2006394. 
[10] 
J. Luo, T. Helleseth and A. Kholosha, Two nonbinary sequences with sixvalued cross correlation, in Proc. IWSDA'11, 2011, 4447. 
[11] 
J, Luo, Y. Tang and H. Wang, Exponential sums, cyclic codes and sequences: the odd characteristic Kasami case,, preprint, (). 
[12] 
G. J. Ness, T. Helleseth and A. Kholosha, On the correlation distribution of the CoulterMatthews decimation, IEEE Trans. Inf. Theory, 52 (2006), 22412247. doi: 10.1109/TIT.2006.872857. 
[13] 
E. Y. Seo, Y. S. Kim, J. S. No and D. J. Shin, Crosscorrelation distribution of pary msequence of period $p^{4k}1$ and its decimated sequences by $(\frac{p^{2k}+1}{2})^{2}$, IEEE Trans. Inf. Theory, 54 (2008),31403149. doi: 10.1109/TIT.2008.924694. 
[14] 
Y. Sun, Z. Wang, H. Li and T. Yan, The crosscorrelation distribution of a $p$ary msequence of period $p^{2k}1$ and its decimated sequence by $\frac{(p^k+1)^2}{2(p^e+1)}$, Adv. Math. Commun., 7 (2013), 409424. doi: 10.3934/amc.2013.7.409. 
[15] 
Y. Xia, C. Li, X. Zeng and T. Helleseth, Some results on crosscorrelation distribution between a $p$ary $m$sequence and its decimated sequences, IEEE Trans. Inf. Theory, 60 (2014), 73687381. doi: 10.1109/TIT.2014.2350775. 
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